In fact, the family of all the maps of the type (REF ) form the set \(\Sigma \)  of the symmetric points of \(C^{\infty }(\mbox{${\mathbb {T}}$},\mathbb {S}^4)\)  with respect to the action of \(G\)  (see [1]}). In our case, \(\Sigma \)  is 2-dimensional and the tangent space to \(\Sigma \)  at a symmetric point \(\Phi _{\eta ,\nu }\)  is generated by
\(\left\lbrace \frac{\partial \Phi _{\eta ,\nu }}{\partial \eta }\,, \frac{\partial \Phi _{\eta ,\nu }}{\partial \nu } \right\rbrace \,.\) 
